Ridge Closed Form by Hand

Two standardised features have X^\top X = \begin{pmatrix} 1 & 0.8 \\ 0.8 & 1 \end{pmatrix} and X^\top y = \begin{pmatrix} 0.9 \\ 0.7 \end{pmatrix} (constants absorbed).

1. Compute the OLS coefficients. Comment on their signs.
2. Compute the ridge coefficients for \lambda = 0.5.
3. Compute the eigenvalues of X^\top X and the ridge shrinkage factor for each eigen-direction at \lambda = 0.5. Explain, in one or two sentences, why ridge handles multicollinearity.